⚛️ Physics & Scientific Computing¶

🔬 ICLR2026 · 69 paper notes

📌 Same area in other venues: 📷 CVPR2026 (2) · 🧪 ICML2026 (33) · 🤖 AAAI2026 (15) · 🧠 NeurIPS2025 (57) · 📹 ICCV2025 (2)

🔥 Top topics: Diffusion Models ×4 · Time-Series Forecasting ×2 · Layout & Composition ×2

A Function-Centric Graph Neural Network Approach for Predicting Electron Densities: This paper proposes Basis Overlap Architecture (BOA)—an equivariant GNN that interprets internal features as "spatial functions expanded in a basis" and passes messages using overlap integrals between atomic basis functions. It represents electron density via a quadratic expansion of basis function products (i.e., density matrix). BOA achieves new SOTA results on QM9 and MD density datasets and generalizes from small molecules (9 heavy atoms) to large systems with nearly 200 atoms.
Accelerating Eigenvalue Dataset Generation via Chebyshev Subspace Filter: Addressing the bottleneck where training neural operators requires massive operator-eigenvalue labeled data generated by expensive numerical solvers, this paper proposes SCSF (Sorting Chebyshev Subspace Filter). SCSF first uses truncated FFT to rank operators with similar spectral distributions in adjacent positions and then utilizes Chebyshev filtering subspace iteration to use the eigenpairs of the "previous problem" as a hot-start for the "next problem." This transforms the entire dataset generation from "independent solving" into a "relay solving" process, achieving up to a 3.5× speedup compared to mainstream solvers.
Accelerating Inference for Multilayer Neural Networks with Quantum Computers: This paper presents the first fully-coherent quantum implementation of multilayer neural networks—transferring ResNet-style multi-filter 2D convolutions, non-linear activations, skip connections, and layer normalization entirely onto quantum circuits without intermediate measurements. Under three quantum data access assumptions, it proves end-to-end inference complexities ranging from quadratic and quartic speedups to \(O(\mathrm{polylog}(N/\epsilon)^k)\) relative to input dimension \(N\).
Adaptive Mamba Neural Operators: AMO explicitly parameterizes the transfer function of Mamba/SSM as orthogonal kernels of the Takenaka-Malmquist (TM) system within a Reproducing Kernel Hilbert Space (RKHS), making the entire network equivalent to an "Adaptive Fourier Decomposition" (AFD). This approach reduces the average relative L2 error by approximately 28% across regular grids, point clouds, irregular domains, and financial PDEs with singularities.
Advancing Universal Deep Learning for Electronic-Structure Hamiltonian Prediction of Materials: NextHAM utilizes a "Step-0 Hamiltonian" as a physical-prior-informed input descriptor, combined with an E(3)-equivariant Transformer and a joint real-space + reciprocal-space training loss. It achieves DFT-level accuracy for electronic structure Hamiltonian prediction across 60+ elements (overall Gauge MAE 1.417 meV, SOC blocks at sub-µeV) and releases Materials-HAM-SOC, a benchmark containing 17,000 structures with spin-orbit coupling.
AQER: A Scalable and Efficient Data Loader for Digital Quantum Computers: This paper unifies various Approximate Quantum Loaders (AQL) into a single optimization problem of "minimizing the distance between the target state and the circuit output state." It proves that the approximate loading error is linearly dominated by a newly proposed entanglement measure \(S\). Based on this, it designs AQER—a method that gradually reduces entanglement by greedily appending two-qubit gate blocks to the circuit, followed by analytical single-qubit rotations and parameter fine-tuning. AQER achieves lower infidelity with fewer two-qubit gates on classical data (MNIST/CIFAR-10/SST-2) and quantum many-body states up to 50 qubits.
ARROW: An Adaptive Rollout and Routing Method for Global Weather Forecasting: ARROW redesigns both the "next-step prediction model" and the "long-term autoregressive rollout strategy" in global weather forecasting: it unifies 6/12/24-hour scales using a multi-interval prediction model and employs a DQN scheduler to adaptively select the next jump based on current weather states, simultaneously reducing error accumulation and preserving fine-grained atmospheric variations in mid-to-long-term forecasts.
ATOM: A Pretrained Neural Operator for Multitask Molecular Dynamics: ATOM reformulates molecular dynamics (MD) prediction as "learning a trajectory operator." It utilizes a quasi-equivariant Transformer neural operator to parallelly decode future atomic coordinates across multiple timestamps. Combined with a self-constructed multi-molecule MD dataset, TG80, for multi-task pretraining, it achieves zero-shot generalization to unseen molecules and unseen time horizons for the first time.
Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction: PRDNet introduces a learnable "pseudo-particle" to simulate crystal diffraction alongside traditional Graph Neural Networks. By synthesizing reciprocal space diffraction patterns using neural-network-generated form factors, it achieves modal-level fusion of graph representations (short-range) and diffraction representations (long-range). While strictly satisfying crystallographic symmetry invariance, it sets new SOTA benchmarks on Materials Project, JARVIS-DFT, and MatBench.
\(\partial^\infty\)-Grid: A Neural Differential Equation Solver with Differentiable Feature Grids: By replacing the common linear interpolation in feature grids with infinitely differentiable Radial Basis Function (RBF) interpolation, fast grid representations—originally designed for "signal fitting"—can stably compute high-order derivatives for the first time. This reduces the training time for solving differential equations such as Poisson, Helmholtz, and Kirchhoff-Love from hours to seconds or minutes (5–20× acceleration) with accuracy comparable to Siren.
CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operators: CFO "borrows" flow matching from generative modeling to learn the right-hand side (RHS) dynamics of time-varying PDEs. By fitting splines to trajectories and using finite differences to estimate temporal derivatives at nodes as velocity field labels, it trains a neural operator to regress this analytical velocity. This bypasses backpropagating through ODE solvers (unlike Neural ODEs), enables training on irregular time grids, and allows inference at arbitrary resolutions. Using only 25% irregularly sampled data, it reduces relative error by up to 87% compared to full-data autoregressive baselines.
ComPhy: Composing Physical Models with end-to-end Alignment: ComPhy decomposes "system-level PDE solving" into "one dedicated module per equation," and links modules sharing physical variables via an end-to-end alignment loss based on derivatives (Jacobian). This transforms the ill-conditioned optimization of single models with multiple losses into a collaborative optimization of simple sub-problems, consistently outperforming PINNs and NCLs on various real physical systems with 2, 3, or 5 equations.
Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges: Proposes Non-Conservative Generalized Schrödinger Bridges (NCGSB)—based on contact Hamiltonian mechanics, which allows energy to change over time. It transforms the bridge problem into geodesic computation on a finite-dimensional Jacobi metric via Contact Wasserstein Geodesic (CWG). Parametrized with ResNet, it achieves near-linear complexity and supports guided generation, significantly outperforming iterative SB solvers on tasks such as manifold navigation, molecular dynamics, and image generation.
Deep Learning for Subspace Regression: This work formalizes the subspace prediction problem in reduced order modeling (ROM) as a regression task on the Grassmann manifold. It proposes specialized loss functions and a subspace embedding technique—predicting a subspace of higher dimension than the target to reduce mapping complexity—achieving significant results in eigenvalue problems, parametric PDEs, and iterative method acceleration.
DGNet: Discrete Green Networks for Data-Efficient Learning of Spatiotemporal PDEs: Based on Green's function theory, the superposition principle is embedded into a physics-neural hybrid architecture to construct Discrete Green Networks (DGNet). It achieves SOTA accuracy using only dozens of training trajectories and demonstrates robust zero-shot generalization to unseen source terms.
Disentangled Representation Learning for Parametric Partial Differential Equations: DisentangO proposes a "Variational Hyper-Neural Operator" architecture that treats the parameters of neural operators for multiple physical systems as signals. It uses a VAE to disentangle identifiable latent physical factors from these black-box parameters. This allows the model to simultaneously perform forward PDE solving (predicting solution fields) and inverse physical discovery (recovering hidden parameters of the driving system), while providing theoretical guarantees for component-wise identifiability.
DRIFT-Net: A Spectral--Coupled Neural Operator for PDEs Learning: The authors propose DRIFT-Net, a dual-branch neural operator that resolves the autoregressive drift issue caused by insufficient global spectral coupling in windowed attention. By combining controlled low-frequency mixing (spectral branch) with local detail fidelity (image branch) via radial gating bandwidth fusion, it reduces errors on Navier-Stokes benchmarks by 7%-54%.
Efficient Regression-based Training of Normalizing Flows for Boltzmann Generators: This paper proposes REGFLOW, which replaces the classic Maximum Likelihood Estimation (MLE) training typically used for Normalizing Flows (NF) with a simple \(\ell_2\) regression objective. By allowing the NF to directly fit noise-data pairs from "known invertible mappings" provided by reflow (pre-trained CNF) or Optimal Transport, REGFLOW bypasses the numerical instability and Jacobian overhead of MLE. For molecular conformational equilibrium sampling, it maintains "one-step sampling + exact likelihood" while significantly outperforming the same NF architectures trained via MLE.
Enhancing Stability of Physics-Informed Neural Network Training Through Saddle-Point Reformulation: This paper reformulates the multi-objective loss reweighting of residual and boundary terms in PINN training as a non-Euclidean non-convex strongly-concave saddle-point problem. By utilizing AdaBGDA to dynamically update network parameters and loss weights, the approach significantly improves training stability and \(L_2\) relative error across 22 PDE benchmarks in PINNacle and 3D Navier-Stokes challenge experiments.
Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs: This paper introduces two restrained structural extensions to the Fourier Neural Operator (FNO): a lightweight hypernetwork to inject physical parameters into each layer's hidden representation, and a Fourier-domain encoder-decoder to mix multiple physical fields. These modifications significantly reduce errors in parameterized and coupled PDE predictions while largely preserving the model scale and training efficiency of the original FNO.
Fast training of accurate physics-informed neural networks without gradient descent: This paper proposes Frozen-PINN, which freezes randomly sampled spatial basis functions and utilizes least squares and adaptive ODE solvers to advance time-varying output layer coefficients. By fundamentally bypassing gradient descent training, it achieves faster training, higher accuracy, and explicit temporal causality across various time-dependent PDEs.
Feedback-driven Recurrent Quantum Neural Network Universality: This work establishes the first quantitative approximation error bounds and universality proofs for feedback-driven Recurrent Quantum Neural Networks (RQNNs). It demonstrates that RQNNs can approximate any fading memory filter using a linear readout layer, with the number of qubits increasing only logarithmically as \(\lceil\log_2(\varepsilon^{-1})\rceil\), effectively avoiding the curse of dimensionality.
FM4NPP: A Scaling Foundation Model for Nuclear and Particle Physics: This work successfully transfers the "large-scale self-supervised pre-training + frozen weights + lightweight adapter" paradigm to sparse, 3D point-cloud-like collider detector data for the first time. Using Mamba, a foundation model FM4NPP with up to 188M parameters was pre-trained on 10 million collision events. With frozen weights and small adapters, it outperforms specialized models across track finding, particle identification (PID), and noise labeling, while demonstrating clear neural scaling laws.
From Cheap Geometry to Expensive Physics: A Physics-agnostic Pretraining Framework for Neural Operators: Utilizing a large amount of "geometry-only, physics-label-free" cheap mesh data, a point cloud VAE is pretrained through the physics-agnostic proxy task of occupancy field reconstruction. The learned latent geometric representations are then fed into Transformer neural operators, significantly improving solution accuracy under scarce PDE labels.
Generalized Spherical Neural Operators: Green's Function Formulation: This paper reformulates spherical neural operators using "designable spherical Green's functions," interpreting the existing SFNO as a special case of relative-position Green's functions. By introducing absolute-position dependent terms, the authors derive the GSNO operator and the multi-scale SHNet, which flexible balance equivariance and invariance, significantly outperforming SOTA models in diffusion MRI, shallow water equations, and global weather forecasting.
GenSR: Symbolic Regression based on Equation Generative Space: GenSR utilizes a dual-branch CVAE to reparameterize the discrete equation space into a generative latent space (a "map" of the equation world) that is "globally symbolic-continuous and locally numerical-smooth." Following an "architecture of map construction \(\rightarrow\) coarse localization \(\rightarrow\) fine search," it employs a degenerate CMA-ES to efficiently find equations in the latent space, reformulating symbolic regression as an ELBO optimization to maximize \(p(\text{Equ.}\mid\text{Num.})\) from a Bayesian perspective.
Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later: GABI utilizes graph autoencoders to distill a geometry-conditioned latent space prior from a large-scale dataset of "geometrically diverse" physical fields. This achieves a "learn first, observe later" paradigm—training requires no knowledge of PDEs, boundary conditions, or observation processes. At inference, this prior is combined with arbitrary observation likelihoods, enabling efficient solution of full-field reconstruction Bayesian inverse problems with well-calibrated uncertainty via ABC sampling.
HSG-12M: A Large-Scale Benchmark of Spatial Multigraphs from the Energy Spectra of Non-Hermitian Crystals: This paper "draws" the energy spectra of non-Hermitian crystals as graphs, proposing the automated pipeline Poly2Graph to map 1D crystalline Hamiltonians to spectral graphs on the complex energy plane. Based on this, HSG-12M is constructed: the first large-scale "spatial multigraph" benchmark (11.6M static + 5.1M dynamic graphs across 1401 classes), exposing new challenges for existing GNNs in learning from multigraph edges that preserve geometric information.
Incomplete Data, Complete Dynamics: A Diffusion Approach: A conditional diffusion framework trainable using only incomplete observations is proposed. By employing a "context-query" partitioning strategy designed according to the observation distribution structure, the diffusion model approximates the conditional expectation of the true complete data without ever seeing full samples. Theoretical guarantees for asymptotic convergence are provided, and the method significantly outperforms existing imputation techniques on sparse physical observations such as fluids and meteorology.
Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study: This study presents the first systematic investigation into initialization schemes for spline-based KANs. It proposes LeCun/Glorot-inspired variance preservation schemes and a tunable power-law initialization family. Large-scale experiments involving over 126K model instances demonstrate that power-law initialization consistently outperforms baselines in function fitting and PDE solving. Furthermore, the Glorot scheme shows significant gains in large-parameter models, with NTK spectral analysis revealing the underlying optimization dynamics.
Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Features: IFeF-PINN extends the hidden layer features of PINNs into random Fourier bases and alternates between "basis function generation" and "linear coefficient regression," significantly mitigating the spectral bias of standard PINNs on high-frequency and multi-scale PDEs.
KANO: Kolmogorov–Arnold Neural Operator: KANO embeds KAN sub-networks into the pseudo-differential operator framework, jointly parameterizing the operator in both frequency and spatial bases. This breaks the pure spectral bottleneck of the Fourier Neural Operator (FNO), enabling robust generalization on variable-coefficient PDEs and allowing the learned operator to be read as closed-form symbolic formulas (coefficient accuracy up to four decimal places).
LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations: LD-EnSF replaces expensive full-space numerical forward simulations with a learnable latent dynamics network (LDNet), migrates the Ensemble Score Filter (EnSF) entirely into an extremely low-dimensional latent space, and aligns sparse irregular observations using a history-aware LSTM encoder. This synergistically accelerates data assimilation by several orders of magnitude while maintaining high precision.
Learning Boltzmann Generators via Constrained Mass Transport: Addressing the common issues of "mass teleportation" and mode collapse in geometric annealing paths during Boltzmann generator training, this work proposes Constrained Mass Transport (CMT). By decomposing direct reverse KL minimization into a sequence of sub-optimization problems that constrain both the KL divergence between adjacent distributions and the entropy decay rate, CMT automatically induces smoother annealing paths. This results in an effective sample size (ESS) over 2.5x higher than SOTA methods without mode collapse.
Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge: Complex PDEs are decomposed into "basic forms" (e.g., pure diffusion or pure convection terms). By training neural operators to simultaneously learn the original PDE and its low-cost basic forms, the model achieves lower error, stable long-term extrapolation, and stronger OOD/sim-to-real generalization using significantly less simulation data.
Learning Escorted Protocols For Multistate Free-Energy Estimation: This paper employs Conditional Flow Matching (CFM) alongside a proposed Conditional Density Matching (CDM) to learn the escorted vector field \(b\) and time-varying potential \(U\) for Escorted Non-Equilibrium (E-NEQ) free-energy estimation. It utilizes Lie-Trotter splitting to reduce work calculation costs and an Escorted Protocol Flow Graph (EPFG) to compress the number of protocols for multistate estimation from \(O(K^2)\) to \(K-1\), achieving higher accuracy than TFEP on the alanine dipeptide (ADP) six-state system.
Learning from the Electronic Structure of Molecules across the Periodic Table: This paper introduces HELM—the first "universal" Hamiltonian matrix prediction model capable of scaling to 100+ atoms, 58 elements, and large basis sets including diffuse functions. It releases the largest molecular Hamiltonian dataset to date, OMol CSH 58k, and demonstrates that transferring shared representations from Hamiltonian pretraining to energy prediction achieves up to ~2× accuracy improvement in low-data scenarios.
Locally Subspace-Informed Neural Operators for Efficient Multiscale PDE Solving: Neural operators (FNO) are used to directly predict the subspace spanned by the multiscale spectral basis functions of GMsFEM. Combined with a subspace-informed loss that aligns subspaces rather than individual basis functions, this approach accelerates the most expensive offline basis function construction phase of GMsFEM by over 60x while preserving the accuracy and reliability of traditional numerical methods.
MatRIS: Toward Reliable and Efficient Pretrained Machine Learning Interatomic Potentials: MatRIS explicitly models three-body (bond angle) interactions using a set of "separable attention" mechanisms with \(O(N)\) complexity. It demonstrates that carefully designed invariant models can achieve or even surpass the accuracy of computationally expensive equivariant models on benchmarks like material discovery, while reducing training costs by 6–13 times.
MoMa: A Simple Modular Learning Framework for Material Property Prediction: MoMa trains each material property task as an independent "module" and stores it in a Hub. For new tasks, it utilizes a training-free, representation-driven algorithm (kNN performance estimation + convex optimization for weights + weight space merging) to adaptively combine the most synergistic modules for fine-tuning. It achieves an average performance gain of 14% over the strongest baseline across 17 material tasks.
Neural Latent Arbitrary Lagrangian-Eulerian Grids for Fluid-Solid Interaction: Fisale integrates the classical numerical ALE (Arbitrary Lagrangian-Eulerian) grids and partitioned coupling algorithms into neural networks. It uses multi-scale "latent ALE grids" to provide a unified geometry-aware representation for fluids, solids, and coupling interfaces. By decomposing the bidirectional FSI into four iterative sub-steps via the Partitioned Coupling Module (PCM)—"update solid → update grid → update fluid → align interface"—it achieves SOTA performance on three realistic 2D/3D bidirectional FSI scenarios.
Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solving: This paper combines the classical Domain Decomposition Method (DDM) with neural operators to propose a "local-to-global" framework. A local neural operator is trained only on randomly generated basic shapes (simple polygons). During inference, an arbitrary geometric domain is partitioned into small subdomains, solved domain-by-domain, and stitched using additive Schwarz iterations (termed Schwarz Neural Inference, SNI). This reduces the relative error on completely unseen geometries from 20%~167% (direct inference) to single digits.
Orbital Transformers for Predicting Wavefunctions in Time-Dependent Density Functional Theory: This paper proposes OrbEvo—an equivariant graph Transformer that learns the time evolution of Kohn-Sham wavefunctions (represented by coefficients of linear combinations of atomic orbitals) for all occupied states in real-time time-dependent density functional theory (RT-TDDFT). It replaces hours of numerical propagation with approximately 1 second of network inference while generalizing across QM9 and accurately recovering dipole moments and absorption spectra.
OrthoSolver: A Neural Proper Orthogonal Decomposition Solver For PDEs: This paper reinterprets the classical Proper Orthogonal Decomposition (POD) from an information-theoretic perspective, proving that the "energy maximization" criterion is equivalent to "mutual information (MI) maximization" under linear Gaussian assumptions. Based on this, it proposes OrthoSolver—a neural operator framework that generalizes POD to nonlinear domains via MI maximization combined with orthogonal regularization to prevent mode collapse, outperforming existing SOTA models across 7 PDE benchmarks.
Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators: Addressing two persistent issues in ViT-based PDE surrogate models—harmonic error accumulation due to fixed patch sizes and "locked-in" compute costs post-training—this paper proposes Overtone. By cyclically switching patch/stride sizes during autoregressive inference, Overtone disperses error from single harmonic frequencies across the entire spectrum. This reduces long-term rollout error by up to 40% without retraining and allows the same model to freely trade off accuracy and speed during inference.
OXtal: An All-Atom Diffusion Model for Organic Crystal Structure Prediction: OXtal is a 100M-parameter all-atom diffusion Transformer that directly samples experimentally realizable 3D crystal structures (molecular conformations + periodic packing) given only the 2D chemical graph of a molecule. By replacing explicit lattice parameterization and equivariant architectures with an "equilibrium-free" stochastic shell sampling training scheme (\(S^4\)) and SE(3) data augmentation, it outperforms existing ML methods for CSP by several orders of magnitude after being trained on 600,000 experimental crystals, while being significantly cheaper than traditional DFT-based methods.
Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems: This paper proposes a post-training framework that fine-tunes a flow-matching generative model, trained solely on observational data, into a "physics-consistent" model. By using weak-form PDE residuals as rewards and leveraging Adjoint Matching to reformulate fine-tuning as a stochastic optimal control problem, the framework introduces an auxiliary "latent parameter" evolution flow. This allows the model to both generate physical fields satisfying PDEs and invert hidden physical parameters (e.g., material coefficients, source terms) even without "solution-parameter" pairs, effectively solving ill-posed inverse problems.
Physics-Informed Inference Time Scaling for Solving High-Dimensional Partial Differential Equations via Defect Correction: SCaSML reformulates the error of a pre-trained PDE surrogate (e.g., PINN or Gaussian Process) as a structure-preserving semilinear PDE. During inference, this "error equation" is solved via Monte Carlo simulation and added back to the initial solution. Without retraining, this approach reduces solution errors for high-dimensional PDEs (up to 160D) by 20–80%, with a theoretical proof that the final error is the product of "surrogate error × simulation error."
Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints: PBFM incorporates PDE residual constraints as a secondary objective during training. It replaces manual loss weighting with Conflict-free Gradients (ConFIG) and eliminates the Jensen gap by reconstructing clean samples through unrolling. This allows Flow Matching to simultaneously approach physics consistency and distributional accuracy without increasing inference overhead, pushing the Pareto front of "Physics vs. Distribution" forward across three PDE benchmarks.
PINFDiT: Energy-Based Physics-Informed Diffusion Transformers for General-purpose Time Series Tasks: PINFDiT utilizes a Diffusion Transformer with a unified masking strategy as a "statistical generalist," then inserts a training-free, architecture-agnostic physical correction step during the inference stage. By treating PDE residuals as energy terms and employing calibrated Langevin dynamics to pull generated samples toward solutions satisfying physical laws, it achieves state-of-the-art (SOTA) performance across scientific time series tasks including forecasting, generation, imputation, anomaly detection, and zero-shot tasks.
PRO-MOF: Policy Optimization with Universal Atomistic Models for Controllable MOF Generation: PRO-MOF decomposes the inverse design of Metal-Organic Frameworks (MOFs) into a two-layer strategy: "selecting chemical building blocks first, then assembling 3D structures." It employs a pre-trained Universal Atomistic Model (UMA) as a high-fidelity physical environment to provide rewards. By rewriting the deterministic Flow Matching generator into a Stochastic Differential Equation (SDE) to support exploration and utilizing a Pass@K version of GRPO to suppress diversity collapse, the method significantly outperforms diffusion models and genetic algorithms in success rates and optimal material quality across three inverse design tasks: \(CO_2\) adsorption, pore size targeting, and minimum energy discovery.
Proximal Diffusion Neural Sampler: This paper proposes PDNS (Proximal Diffusion Neural Sampler), which models "sampling from unnormalized target distributions" as a stochastic optimal control problem in path measure space. It utilizes the Proximal Point Method to decompose a one-shot global optimization into a sequence of sub-problems with KL proximity constraints. This allows the sampler to gradually approach the target along a geometric interpolation path between \(\pi\) and a reference distribution, alleviating mode collapse in strongly multi-modal tasks (Molecular Dynamics, Ising/Potts, etc.) and achieving SOTA on multiple continuous and discrete benchmarks.
RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data: RealPDEBench is the first scientific machine learning benchmark that packages real-world experimental measurement data alongside paired numerical simulation data. Covering 5 complex physical systems, 3 task categories, 9 metrics, and 10 baselines, it systematically reveals the significant gap between simulation and real-world data and demonstrates that "pre-training on simulation followed by fine-tuning on real data" consistently improves both accuracy and convergence speed.
Riesz Neural Operator for Solving Partial Differential Equations: RNO introduces the Riesz transform into neural operators, utilizing directional derivative channels in the frequency domain to compensate for the inability of FNO/LNO to model local non-stationary details. It simultaneously improves accuracy, robustness, and efficiency across various PDEs, Navier-Stokes, and ERA5 weather data.
Robust and Interpretable Adaptation of Equivariant Materials Foundation Models via Sparsity-promoting Fine-tuning: This paper proposes a sparsity-promoting fine-tuning method that, while strictly maintaining equivariance, updates only approximately 0.5–3% of path weight parameters in Materials Foundation Models (MLIPs). It achieves or exceeds the energy/force prediction accuracy of full fine-tuning and ELoRA on molecular, crystal, and magnetic systems, while the resulting sparse update patterns provide physical interpretability (e.g., d-orbital channels are specifically modified in transition metal systems).
SAQ: Stabilizer-Aware Quantum Error Correction Decoder: SAQ-Decoder utilizes a stabilizer-aware dual-stream Transformer to learn the mapping from syndromes to logical error classes and physical correction operations. By incorporating Constraint-Projected Nullspace Descent (CPND) post-processing to ensure syndrome consistency, it pushes the thresholds for independent and depolarizing noise on toric codes to 10.99% and 18.6%, respectively, approaching the maximum likelihood decoding upper bound.
Scaling Laws and Symmetry, Evidence from Neural Force Fields: This paper conducts systematic scaling law experiments on geometric tasks for "Neural Network Interatomic Potentials (NNIP)". It finds that power-law exponents are architecture-dependent: architectures with stronger rotation/permutation symmetry and higher tensor orders exhibit larger scaling exponents with respect to data, parameters, and compute. Consequently, performance gaps widen rather than narrow at scale, providing counter-evidence to the popular view that equivariance should be abandoned in favor of large-scale models learning symmetries themselves.
Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems: This paper reformulates "learning evolution operators for high-dimensional dynamical systems" as an encoder-only self-supervised contrastive learning problem. By using bilinear similarity \(\langle\phi(x_t), P\phi(x_{t+1})\rangle\) to model the density ratio of state transitions, the authors prove it is equivalent to least-squares operator estimation and negative VAMP-2 scores under an optimal predictor. The method automatically extracts interpretable slow modes across three large-scale scientific systems—protein folding, molecular binding, and global climate (ENSO)—enabling cross-system representation transfer.
Spectral-Guided Physical Dynamics Distillation: Addressing the challenge of predicting long-term 3D trajectories of particles given only the initial state, this paper proposes SGDD: using a teacher encoder that observes future trajectories as "privileged information" to adaptively weight key frequency components in a unified spatiotemporal spectral domain, and then distilling this dynamics-rich representation into a student encoder that only sees the initial state, achieving more accurate and stable long-term predictions across multi-scale systems including molecules, proteins, and human motion.
Stretching Beyond the Obvious: A Gradient-Free Framework to Unveil the Hidden Landscape of Visual Invariance: Proposes the Stretch-and-Squeeze (SnS) algorithm, a gradient-free, model-agnostic bi-objective optimization framework that systematically probes the invariance manifold of visual systems by "stretching" representations at different processing levels while "squeezing" target unit activations, revealing hierarchical differences in invariance interpretability between standard and robust CNNs.
Sublinear Time Quantum Algorithm for Attention Approximation: Propose the first quantum data structure with sublinear time complexity relative to sequence length \(n\) for approximating row queries of the Transformer attention matrix. The preprocessing time is \(\widetilde{O}(\epsilon^{-1} n^{0.5} \cdot \text{poly}(d, s_\lambda, \alpha))\), and each row query takes \(\widetilde{O}(s_\lambda^2 + s_\lambda d)\), achieving a quadratic speedup over classical algorithms regarding \(n\).
TandemFoilSet: Datasets for Flow Field Prediction of Tandem-Airfoil Through the Reuse of Single Airfoils: This paper introduces the first tandem-airfoil flow field prediction dataset, TandemFoilSet (consisting of 8104 CFD cases, with 4152 tandem configurations paired with corresponding single-airfoil data). It provides a curriculum learning benchmark centered on "reusing single-airfoil data"—utilizing freestream as a physical prior for residual pre-training, performing smooth-combining of single-airfoil predictions as estimate fields, and employing multi-network (multi-NN) sub-domain inference, reducing GNN baseline prediction errors by approximately 65%.
Test-Time Accuracy-Cost Control in Neural Simulators via Recurrent-Depth: This paper proposes RecurrSim (Recurrent-Depth Simulator)—a model-agnostic "Encoder + Recurrent Block + Decoder" framework. It enables a trained neural PDE simulator to slide between accuracy and computational cost during inference using a single knob \(K\) (iteration count) without retraining or architectural changes. On multiple fluid dynamics benchmarks, it achieves or exceeds larger baselines and diffusion-based adaptive methods with fewer parameters and lower VRAM.
The False Promise of Zero-Shot Super-Resolution in Machine-Learned Operators: This paper systematically refutes the promise of "zero-shot super-resolution" for Machine-Learned Operators (MLOs) such as the Fourier Neural Operator (FNO). By decomposing multi-resolution inference into two sub-capabilities—"resolution interpolation" and "frequency information extrapolation"—the authors find that FNO fails at both and exhibits severe aliasing. Neither physical constraints nor band-limited learning effectively addresses this issue. Finally, a simple yet effective multi-resolution training protocol is proposed, achieving robust cross-resolution generalization using a minimal amount of high-resolution data.
Towards a Transferable Acceleration Method for Density Functional Theory: Addressing the bottleneck of slow Self-Consistent Field (SCF) iterations in Density Functional Theory (DFT), this work departs from the mainstream approach of predicting the Hamiltonian matrix. Instead, it utilizes an E(3) equivariant network to predict the expansion coefficients of the electron density under a compact auxiliary basis and provides a complete pipeline to transform this density into an SCF initial guess. Trained only on small molecules with fewer than 20 atoms, the model directly reduces the SCF iterations of 60-atom molecules by 33.3% on average and can accelerate polymer/peptide systems with up to 900 atoms without retraining, whereas Hamiltonian-based baselines often fail to converge on large molecules.
Tucker-FNO: Tensor Tucker-Fourier Neural Operator and its Universal Approximation Theory: This paper employs Tucker tensor decomposition to decompose high-dimensional Fourier Neural Operators (FNO) into a set of 1D FNOs, replacing \(d\)-dimensional FFTs with \(d\) one-dimensional FFTs. This reduces the FFT complexity for 3D PDEs from \(O(d_v n^3 \log n^3)\) to \(O(3 d_v n \log n)\). This work provides the first proof that such tensor-decomposed FNOs still satisfy the Universal Approximation Theorem and achieves both faster and more accurate results in high-dimensional PDEs (Navier-Stokes / Plasticity / Burgers) and image/video signal recovery.
Uncertainty-Aware Diagnostics for Physics-Informed Machine Learning: This paper proposes Physics-Informed Log Evidence (PILE) within the Gaussian Process framework of physics-informed kernel learning. It uses a marginal likelihood index with an uncertainty interpretation to uniformly diagnose data fitting, physical constraints, and kernel/regularization hyperparameter selection, avoiding the multi-objective tuning ambiguity common in PIML.
(U)NFV: (Un)supervised Neural Finite Volume Methods for Solving Hyperbolic PDEs: This work replaces the "hand-designed numerical flux" in the classic Finite Volume (FV) method with a lightweight CNN. By preserving the conservative update structure of FV, it learns flux approximations across larger spatio-temporal stencils. It supports both supervised training (NFV) and unsupervised training via weak-form residuals (UNFV). On 1D hyperbolic conservation laws, the error is up to 10x lower than the Godunov scheme, approaching Discontinuous Galerkin (DG) performance while maintaining the implementation complexity of standard FV.
VisionLaw: Inferring Interpretable Intrinsic Dynamics from Visual Observations via Bilevel Optimization: VisionLaw models the task of "inferring physical properties from videos" as a bilevel optimization problem—the upper level employs an LLM as a physics expert to evolve symbolic constitutive laws (Python code), while the lower level uses a differentiable MPM simulator to optimize continuous material parameters under visual supervision, returning fitness and feedback. This approach infers both interpretable and generalizable intrinsic dynamics from single-view videos, reducing Chamfer distance on synthetic data from NeuMA's 2.86 to 1.65.